Metrics for sqrt D (should all be same)

analyze1.1s (27.3%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	199.9%	-99.9%	0%	0%	0%	1
0%	0%	399.8%	-299.8%	0%	0%	0%	2
0%	0%	799.6%	-699.6%	0%	0%	0%	3
0%	0%	1599.2%	-1499.2%	0%	0%	0%	4
0%	0%	3198.4%	-3098.4%	0%	0%	0%	5
0%	0%	6396.9%	-6296.9%	0%	0%	0%	6
0%	0%	12793.8%	-12693.8%	0%	0%	0%	7
0%	0%	25587.5%	-25487.5%	0%	0%	0%	8
0%	0%	51175%	-51075%	0%	0%	0%	9
0%	0%	102350%	-102250%	0%	0%	0%	10
0%	0%	204700%	-204600%	0%	0%	0%	11
0%	0%	409400%	-409300%	0%	0%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample1.2s (28.6%)

Results

1.2s	8253×	body	256	valid
0.0ms	3×	body	256	infinite

Bogosity

preprocess121.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1792×	`fma-def`
1318×	`fma-neg`
1110×	`distribute-lft-neg-in`
808×	`distribute-rgt-neg-in`
638×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	34
1	26	34
2	53	34
3	193	34
4	830	34
5	1875	34
6	3861	34
7	5203	34
8	6430	34
9	7545	34

Stop Event

1×	node limit

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(sqrt.f64 (*.f64 2 (pow.f64 (neg.f64 x) 2)))

Outputs
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 x (.f64 x -2)))
(sqrt.f64 (*.f64 2 (pow.f64 (neg.f64 x) 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 x (.f64 x -2)))

Symmetry

(abs x)

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify235.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

2734×	`sqr-pow`
1306×	`cube-prod`
1044×	`pow-sqr`
884×	`associate-r`
868×	`unswap-sqr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	14	17
2	25	17
3	46	17
4	106	17
5	329	17
6	1230	17
7	2094	17
8	2234	17
9	2402	17
10	2599	17
11	2878	17
12	3246	17
13	3692	17
14	4220	17
15	4862	17
16	5641	17
17	5967	17
18	6241	17
19	6447	17
20	6507	17
21	6537	17
22	7472	17

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Outputs
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))

eval2.0ms (0.1%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Accurracy

53.3%

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.3%	(sqrt.f64 (.f64 2 (.f64 x x)))
▶	53.3%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize121.0ms (3%)

Local Accuracy

Found 2 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(.f64 2 (.f64 x x))
✓	53.3%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 18 to 9 computations (50% saved)

series7.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(sqrt.f64 (.f64 2 (.f64 x x)))
1.0ms	x	@	inf	(sqrt.f64 (.f64 2 (.f64 x x)))
1.0ms	x	@	0	(.f64 2 (.f64 x x))
1.0ms	x	@	inf	(.f64 2 (.f64 x x))
1.0ms	x	@	-inf	(.f64 2 (.f64 x x))

rewrite182.0ms (4.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1354×	`pow1`
1244×	`add-exp-log`
1244×	`log1p-expm1-u`
1244×	`expm1-log1p-u`
1214×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	160	24
2	1810	24

Stop Event

1×	node limit

Counts

2 → 36

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 2 (.f64 x x))

Outputs
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(*.f64 x (sqrt.f64 2))
(.f64 (.f64 x (sqrt.f64 2)) 1)
(.f64 1 (.f64 x (sqrt.f64 2)))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(.f64 (pow.f64 1 1/2) (.f64 x (sqrt.f64 2)))
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4)) 1/2) (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/2))
(.f64 (pow.f64 (.f64 2 x) 1/2) (sqrt.f64 x))
(pow.f64 (.f64 2 (.f64 x x)) 1/2)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(-.f64 (+.f64 1 (.f64 2 (.f64 x x))) 1)
(pow.f64 (.f64 2 (.f64 x x)) 1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3)
(pow.f64 (*.f64 (pow.f64 x 4) 4) 1/2)
(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 3) 1/3)
(sqrt.f64 (*.f64 (pow.f64 x 4) 4))
(log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 2))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 x x)) 3))
(expm1.f64 (log1p.f64 (.f64 2 (.f64 x x))))
(exp.f64 (log.f64 (.f64 2 (.f64 x x))))
(log1p.f64 (expm1.f64 (.f64 2 (.f64 x x))))

simplify125.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1200×	`log-prod`
1148×	`fma-def`
1056×	`distribute-rgt-in`
1030×	`distribute-lft-in`
700×	`fma-neg`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	816
1	193	816
2	739	816
3	2412	688
4	7441	688

Stop Event

1×	node limit

Counts

60 → 48

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(*.f64 x (sqrt.f64 2))
(.f64 (.f64 x (sqrt.f64 2)) 1)
(.f64 1 (.f64 x (sqrt.f64 2)))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(.f64 (pow.f64 1 1/2) (.f64 x (sqrt.f64 2)))
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4)) 1/2) (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/2))
(.f64 (pow.f64 (.f64 2 x) 1/2) (sqrt.f64 x))
(pow.f64 (.f64 2 (.f64 x x)) 1/2)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(-.f64 (+.f64 1 (.f64 2 (.f64 x x))) 1)
(pow.f64 (.f64 2 (.f64 x x)) 1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3)
(pow.f64 (*.f64 (pow.f64 x 4) 4) 1/2)
(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 3) 1/3)
(sqrt.f64 (*.f64 (pow.f64 x 4) 4))
(log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 2))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 x x)) 3))
(expm1.f64 (log1p.f64 (.f64 2 (.f64 x x))))
(exp.f64 (log.f64 (.f64 2 (.f64 x x))))
(log1p.f64 (expm1.f64 (.f64 2 (.f64 x x))))

Outputs
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 (.f64 x (sqrt.f64 2)) 1)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 1 (.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (sqrt.f64 (cbrt.f64 (*.f64 x (+.f64 x x)))))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(.f64 (pow.f64 1 1/2) (.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4)) 1/2) (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/2))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (sqrt.f64 (cbrt.f64 (*.f64 x (+.f64 x x)))))
(.f64 (pow.f64 (.f64 2 x) 1/2) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(pow.f64 (.f64 2 (.f64 x x)) 1/2)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(-.f64 (+.f64 1 (.f64 2 (.f64 x x))) 1)
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(pow.f64 (.f64 2 (.f64 x x)) 1)
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3)
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(pow.f64 (*.f64 (pow.f64 x 4) 4) 1/2)
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 3) 1/3)
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(sqrt.f64 (*.f64 (pow.f64 x 4) 4))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 2))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 x x)) 3))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(expm1.f64 (log1p.f64 (.f64 2 (.f64 x x))))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(exp.f64 (log.f64 (.f64 2 (.f64 x x))))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(log1p.f64 (expm1.f64 (.f64 2 (.f64 x x))))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))

eval19.0ms (0.5%)

Compiler: Compiled 375 to 272 computations (27.5% saved)

prune17.0ms (0.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	46	2	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	2	49

Accurracy

100.0%

Counts

49 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	99.4%	(*.f64 (sqrt.f64 2) x)
▶	100.0%	(hypot.f64 x x)
▶	99.4%	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize76.0ms (1.9%)

Local Accuracy

Found 2 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.4%	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 14 to 9 computations (35.7% saved)

series4.0ms (0.1%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(hypot.f64 x x)
1.0ms	x	@	inf	(hypot.f64 x x)
1.0ms	x	@	0	(hypot.f64 x x)
0.0ms	x	@	-inf	(*.f64 (sqrt.f64 2) x)
0.0ms	x	@	inf	(*.f64 (sqrt.f64 2) x)

rewrite108.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1218×	`pow1`
1118×	`add-exp-log`
1118×	`log1p-expm1-u`
1118×	`expm1-log1p-u`
1092×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	159	14
2	1784	14

Stop Event

1×	node limit

Counts

2 → 40

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)

Outputs
(-.f64 (+.f64 1 (hypot.f64 x x)) 1)
(pow.f64 (hypot.f64 x x) 1)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(pow.f64 (.f64 2 (.f64 x x)) 1/2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(exp.f64 (log.f64 (hypot.f64 x x)))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
(-.f64 (+.f64 1 (hypot.f64 x x)) 1)
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (hypot.f64 x x) 1)
(*.f64 1 (hypot.f64 x x))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (sqrt.f64 2)))
(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
(.f64 (cbrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 2)) x))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sqrt.f64 2)))
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 x (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(.f64 (.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))
(pow.f64 (hypot.f64 x x) 1)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(pow.f64 (.f64 2 (.f64 x x)) 1/2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(exp.f64 (log.f64 (hypot.f64 x x)))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))

simplify105.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1050×	`log-prod`
786×	`fma-neg`
712×	`exp-prod`
604×	`*-commutative`
600×	`fma-def`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	848
1	135	692
2	384	536
3	2022	536
4	4378	536
5	6366	536

Stop Event

1×	node limit

Counts

52 → 35

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(-.f64 (+.f64 1 (hypot.f64 x x)) 1)
(pow.f64 (hypot.f64 x x) 1)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(pow.f64 (.f64 2 (.f64 x x)) 1/2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(exp.f64 (log.f64 (hypot.f64 x x)))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
(-.f64 (+.f64 1 (hypot.f64 x x)) 1)
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (hypot.f64 x x) 1)
(*.f64 1 (hypot.f64 x x))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (sqrt.f64 2)))
(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
(.f64 (cbrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 2)) x))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sqrt.f64 2)))
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 x (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(.f64 (.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))
(pow.f64 (hypot.f64 x x) 1)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(pow.f64 (.f64 2 (.f64 x x)) 1/2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(exp.f64 (log.f64 (hypot.f64 x x)))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(-.f64 (+.f64 1 (hypot.f64 x x)) 1)
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (hypot.f64 x x) 1)
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (.f64 2 (.f64 x x)) 1/2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(hypot.f64 x x)
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(exp.f64 (log.f64 (hypot.f64 x x)))
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(-.f64 (+.f64 1 (hypot.f64 x x)) 1)
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 (hypot.f64 x x) 1)
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(*.f64 1 (hypot.f64 x x))
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (cbrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 x (cbrt.f64 (sqrt.f64 2))))
(.f64 x (.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(*.f64 (sqrt.f64 2) x)
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 x (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(.f64 (cbrt.f64 2) (.f64 x (cbrt.f64 (sqrt.f64 2))))
(.f64 x (.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(.f64 (.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))
(*.f64 (sqrt.f64 2) x)
(pow.f64 (hypot.f64 x x) 1)
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (.f64 2 (.f64 x x)) 1/2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(exp.f64 (log.f64 (hypot.f64 x x)))
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
(+.f64 (+.f64 1 (hypot.f64 x x)) -1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)

eval26.0ms (0.6%)

Compiler: Compiled 237 to 139 computations (41.4% saved)

prune16.0ms (0.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	35	2	37

Accurracy

100.0%

Counts

37 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.4%	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 29 to 20 computations (31% saved)

regimes50.0ms (1.2%)

Accuracy

Total -30.1b remaining (-257014.7%)

Threshold costs -30.1b (-257014.7%)

Counts

4 → 1

Calls

Call 1

Inputs
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Outputs
(hypot.f64 x x)

Calls

4 calls:

16.0ms	(*.f64 2 (pow.f64 x 2))
11.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
10.0ms	(pow.f64 x 2)
10.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (*.f64 2 (pow.f64 x 2)))`
100.0%	1	`(*.f64 2 (pow.f64 x 2))`
100.0%	1	`(pow.f64 x 2)`

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(hypot.f64 x x)

Outputs
(hypot.f64 x x)

Compiler

Compiled 4 to 2 computations (50% saved)

soundness506.0ms (12.3%)

Rules

2734×	`sqr-pow`
1306×	`cube-prod`
1200×	`log-prod`
1148×	`fma-def`
1056×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	14	17
2	25	17
3	46	17
4	106	17
5	329	17
6	1230	17
7	2094	17
8	2234	17
9	2402	17
10	2599	17
11	2878	17
12	3246	17
13	3692	17
14	4220	17
15	4862	17
16	5641	17
17	5967	17
18	6241	17
19	6447	17
20	6507	17
21	6537	17
22	7472	17
0	83	816
1	193	816
2	739	816
3	2412	688
4	7441	688

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 93 to 65 computations (30.1% saved)

end0.0ms (0%)

preprocess75.0ms (1.8%)

Remove: (abs x)
Compiler: Compiled 30 to 20 computations (33.3% saved)

analyze1.1s (27.3%)

sample1.2s (28.6%)

preprocess121.0ms (3%)

simplify235.0ms (5.7%)

eval2.0ms (0.1%)

prune5.0ms (0.1%)

localize121.0ms (3%)

series7.0ms (0.2%)

rewrite182.0ms (4.4%)

simplify125.0ms (3%)

eval19.0ms (0.5%)

prune17.0ms (0.4%)

localize76.0ms (1.9%)

series4.0ms (0.1%)

rewrite108.0ms (2.6%)

simplify105.0ms (2.5%)

eval26.0ms (0.6%)

prune16.0ms (0.4%)

regimes50.0ms (1.2%)

simplify10.0ms (0.2%)

soundness506.0ms (12.3%)

end0.0ms (0%)

preprocess75.0ms (1.8%)

Profiling